Question

The mass and volume of a body are $4.37g$ and $2.5c{{m}^{3}}$ respectively. The density of the material of the body to correct significant figures is
$\begin{align}
  & A)1.604gc{{m}^{-3}} \\
 & B)1.69gc{{m}^{-3}} \\
 & C)1.7gc{{m}^{-3}} \\
 & D)1.695gc{{m}^{-3}} \\
\end{align}$

Answer 1

Hint: Density of a body refers to the degree of compactness of molecules in that body. For example, water is said to be denser than oil because a greater number of water molecules can occupy a unit volume than the number of oil molecules, which can occupy the same unit volume. Density of the material of a body varies with temperature as well as pressure. Mathematically, density is defined as the ratio of mass of the body to the volume of the body. To express a physical quantity to correct significant figures refers to express the quantity in minimum possible significant figures. Significant figure refers to the necessary and important numbers required to express a physical quantity
Formula used:
$\rho =\dfrac{M}{V}$

Complete answer:
Mass of a body refers to the heaviness of the body whereas volume of a body refers to the space occupied by the body. The SI unit of mass is $kg$ while the SI unit of volume is ${{m}^{3}}$. Density of the material of a body is defined as the ratio of mass of the body to the volume of the body. The SI unit of density is $kg{{m}^{-3}}$. Mathematically, density of a body is represented by
$\rho =\dfrac{M}{V}$
where
$\rho $ is the density of the material of a body
$M$ is the mass of the body
$V$ is the volume of the body
Let this be equation 1.
Coming to our question, we are provided with a body whose mass and volume are $4.37g$ and $2.5c{{m}^{3}}$ respectively. We are required to determine the density of the material of the body to correct significant figures.
Clearly, we are given that
$M=4.37g$ is the mass of the body
$V=2.5c{{m}^{3}}$ is the volume of the body
Using equation 1, density $\rho $ of the given body is
$\rho =\dfrac{M}{V}=\dfrac{4.37g}{2.5c{{m}^{3}}}=1.748gc{{m}^{-3}}$
Let this be equation 2.
Now, we need to express this result to correct significant figures, to cross-check with the given options.
Expressing a quantity in correct significant figures refers to expressing the quantity in minimum possible significant figures.
Clearly, the minimum possible significant figures in the result given by equation 2 are two. Therefore, density of the body can be expressed as
$\rho =1.7gc{{m}^{-3}}$

So, the correct answer is “Option C”.

Note:
Students need to be thorough with the concept of expressing a quantity in correct significant figures. For example, a density of $033.0296gc{{m}^{-3}}$ in correct significant figures is expressed as $33.03gc{{m}^{-3}}$. Here, it is clear that the minimum possible significant figures to express the first given density is three. After proper rounding-off, the final density is expressed accordingly, with three significant figures.